Statistical Relationship between Quantitative and Dichotomous Variables: Student’s Test and Moving Average Approach

Document Type : Original Article

Authors
Anatoly Nikolaevich Varaksin 1
Tatiana Anatolyevna Maslakova 1
Ekaterina Danilovna Konstantinova 1
Yulia Valeryevna Shalaumova 2
1 Federal state budgetary institution of science "Institute of Industrial Ecology" Ural Branch of the Russian Academy of Sciences
2 Institute of Industrial Ecology, Ural Branch of the Russian Academy of Sciences
10.22034/jirss.2023.707641
Abstract
A new technique is proposed for evaluating the statistical relationship between a quantitative variable Y and a dichotomous variable X assuming two values: X=0 and X=1. The technique is based on the division of the quantitative variable Y into strata by the moving average technique and computation of average values in the strata for the variables Y and X. Stratification turns the dichotomous variable X into a quantitative one. Once the variable X has been transformed in this way, the statistical relationship between Y and X may be analyzed by linear regression and by analysis of variance. Thus, the technique proposed expands the range of methods available for analyzing statistical relationships between quantitative and dichotomous variables. Specific examples are used to compare the moving average technique with the t-test for symmetric (normal) and asymmetric distributions of quantitative variable Y. It is shown that the statistical relationship between stratified Y and X can be strongly different for a symmetrically (normally) distributed variable Y.
Keywords
Analysis of Variance
Body Mass Index
Linear Regression
Moving Average
Smoking
Stress Index
Student’s Test
Quantitative Predictor and Dichotomous Outcome
Subjects
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Journal of the Iranian Statistical Society
Volume 22, Issue 1
June 2023
Pages 123-135

  • Receive Date 28 March 2023
  • Revise Date 22 June 2023
  • Accept Date 15 September 2023